PyBEAM: A Bayesian approach to parameter inference for a wide class of binary evidence accumulation models.

Many decision-making theories are encoded in a class of processes known as evidence accumulation models (EAM). These assume that noisy evidence stochastically accumulates until a set threshold is reached, triggering a decision. One of the most successful and widely used of this class is the Diffusion Decision Model (DDM). The DDM however is limited in scope and does not account for processes such as evidence leakage, changes of evidence, or time varying caution. More complex EAMs can encode a wider array of hypotheses, but are currently limited by computational challenges. In this work, we develop the Python package PyBEAM (Bayesian Evidence Accumulation Models) to fill this gap. Toward this end, we develop a general probabilistic framework for predicting the choice and response time distributions for a general class of binary decision models. In addition, we have heavily computationally optimized this modeling process and integrated it with PyMC, a widely used Python package for Bayesian parameter estimation. This 1) substantially expands the class of EAM models to which Bayesian methods can be applied, 2) reduces the computational time to do so, and 3) lowers the entry fee for working with these models. Here we demonstrate the concepts behind this methodology, its application to parameter recovery for a variety of models, and apply it to a recently published data set to demonstrate its practical use.

Cortical tension initiates the positive feedback loop between cadherin and F-actin.

Adherens junctions physically link two cells at their contact interface via extracellular binding between cadherin molecules and intracellular interactions between cadherins and the actin cytoskeleton. Cadherin and actomyosin cytoskeletal dynamics are regulated reciprocally by mechanical and chemical signals, which subsequently determine the strength of cell-cell adhesions and the emergent organization and stiffness of the tissues they form. However, an understanding of the integrated system is lacking. We present a new mechanistic computational model of intercellular junction maturation in a cell doublet to investigate the mechanochemical cross talk that regulates adherens junction formation and homeostasis. The model couples a two-dimensional lattice-based simulation of cadherin dynamics with a reaction-diffusion representation of the reorganising actomyosin network through its regulation by Rho signalling at the intracellular junction. We demonstrate that local immobilization of cadherin induces cluster formation in a cis-less-dependent manner. We then recapitulate the process of cell-cell contact formation. Our model suggests that cortical tension applied on the contact rim can explain the ring distribution of cadherin and actin filaments (F-actin) on the cell-cell contact of the cell doublet. Furthermore, we propose and test the hypothesis that cadherin and F-actin interact like a positive feedback loop, which is necessary for formation of the ring structure. Different patterns of cadherin distribution were observed as an emergent property of disturbances of this positive feedback loop. We discuss these findings in light of available experimental observations on underlying mechanisms related to cadherin/F-actin binding and the mechanical environment.

Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis.

The clustering of membrane-bound proteins facilitates their transport by cortical actin flow in early Caenorhabditis elegans embryo cell polarity. PAR-3 clustering is critical for this process, yet the biophysical processes that couple protein clusters to cortical flow remain unknown. We develop a discrete, stochastic agent-based model of protein clustering and test four hypothetical models for how clusters may interact with the flow. Results show that the canonical way to assess transport characteristics from single-particle tracking data used thus far in this area, the Péclet number, is insufficient to distinguish these hypotheses and that all models can account for transport characteristics quantified by this measure. However, using this model, we demonstrate that these different cluster-cortex interactions may be distinguished using a different metric, namely the scalar projection of cluster displacement on to the flow displacement vector. Our results thus provide a testable way to use existing single-particle tracking data to test how endogenous protein clusters may interact with the cortical flow to localize during polarity establishment. To facilitate this investigation, we also develop both improved simulation and semi-analytic methodologies to quantify motion summary statistics (e.g., Péclet number and scalar projection) for these stochastic models as a function of biophysical parameters.

Simple Rho GTPase Dynamics Generate a Complex Regulatory Landscape Associated with Cell Shape.

Migratory cells exhibit a variety of morphologically distinct responses to their environments that manifest in their cell shape. Some protrude uniformly to increase substrate contacts, others are broadly contractile, some polarize to facilitate migration, and yet others exhibit mixtures of these responses. Prior studies have identified a discrete collection of shapes that the majority of cells display and demonstrated that activity levels of the cytoskeletal regulators Rac1 and RhoA GTPase regulate those shapes. Here, we use computational modeling to assess whether known GTPase dynamics can give rise to a sufficient diversity of spatial signaling states to explain the observed shapes. Results show that the combination of autoactivation and mutually antagonistic cross talk between GTPases, along with the conservative membrane binding, generates a wide array of distinct homogeneous and polarized regulatory phenotypes that arise for fixed model parameters. From a theoretical perspective, these results demonstrate that simple GTPase dynamics can generate complex multistability in which six distinct stable steady states (three homogeneous and three polarized) coexist for a fixed set of parameters, each of which naturally maps to an observed morphology. From a biological perspective, although we do not explicitly model the cytoskeleton or resulting cell morphologies, these results, along with prior literature linking GTPase activity to cell morphology, support the hypothesis that GTPase signaling dynamics can generate the broad morphological characteristics observed in many migratory cell populations. Further, the observed diversity may be the result of cells populating a complex morphological landscape generated by GTPase regulation rather than being the result of intrinsic cell-cell variation. These results demonstrate that Rho GTPases may have a central role in regulating the broad characteristics of cell shape (e.g., expansive, contractile, polarized, etc.) and that shape heterogeneity may be (at least partly) a reflection of the rich signaling dynamics regulating the cytoskeleton rather than intrinsic cell heterogeneity.

Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells.

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.

Microtubules Regulate Localization and Availability of Insulin Granules in Pancreatic Beta Cells.

Two key prerequisites for glucose-stimulated insulin secretion (GSIS) in ß cells are the proximity of insulin granules to the plasma membrane and their anchoring or docking to the plasma membrane (PM). Although recent evidence has indicated that both of these factors are altered in the context of diabetes, it is unclear what regulates localization of insulin granules and their interactions with the PM within single cells. Here, we demonstrate that microtubule (MT)-motor-mediated transport dynamics have a critical role in regulating both factors. Super-resolution imaging shows that whereas the MT cytoskeleton resembles a random meshwork in the cells' interior, MTs near the cell surface are preferentially aligned with the PM. Computational modeling suggests two consequences of this alignment. First, this structured MT network preferentially withdraws granules from the PM. Second, the binding and transport of insulin granules by MT motors prevents their stable anchoring to the PM. These findings suggest the MT cytoskeleton may negatively regulate GSIS by both limiting the amount of insulin proximal to the PM and preventing or breaking interactions between the PM and the remaining nearby insulin granules. These results predict that altering MT network structure in ß cells can be used to tune GSIS. Thus, our study points to the potential of an alternative therapeutic strategy for diabetes by targeting specific MT regulators.

Mechanochemical feedback underlies coexistence of qualitatively distinct cell polarity patterns within diverse cell populations.

Cell polarization and directional cell migration can display random, persistent, and oscillatory dynamic patterns. However, it is not clear whether these polarity patterns can be explained by the same underlying regulatory mechanism. Here, we show that random, persistent, and oscillatory migration accompanied by polarization can simultaneously occur in populations of melanoma cells derived from tumors with different degrees of aggressiveness. We demonstrate that all of these patterns and the probabilities of their occurrence are quantitatively accounted for by a simple mechanism involving a spatially distributed, mechanochemical feedback coupling the dynamically changing extracellular matrix (ECM)-cell contacts to the activation of signaling downstream of the Rho-family small GTPases. This mechanism is supported by a predictive mathematical model and extensive experimental validation, and can explain previously reported results for diverse cell types. In melanoma, this mechanism also accounts for the effects of genetic and environmental perturbations, including mutations linked to invasive cell spread. The resulting mechanistic understanding of cell polarity quantitatively captures the relationship between population variability and phenotypic plasticity, with the potential to account for a wide variety of cell migration states in diverse pathological and physiological conditions.

A parameter recovery assessment of time-variant models of decision-making.

Evidence accumulation models have been one of the most dominant modeling frameworks used to study rapid decision-making over the past several decades. These models propose that evidence accumulates from the environment until the evidence for one alternative reaches some threshold, typically associated with caution, triggering a response. However, researchers have recently begun to reconsider the fundamental assumptions of how caution varies with time. In the past, it was typically assumed that levels of caution are independent of time. Recent investigations have however suggested the possibility that levels of caution decrease over time and that this strategy provides more efficient performance under certain conditions. Our study provides the first comprehensive assessment of this newer class of models accounting for time-varying caution to determine how robustly their parameters can be estimated. We assess five overall variants of collapsing threshold/urgency signal models based on the diffusion decision model, linear ballistic accumulator model, and urgency gating model frameworks. We find that estimation of parameters, particularly those associated with caution/urgency modulation are most robust for the linearly collapsing threshold diffusion model followed by an urgency-gating model with a leakage process. All other models considered, particularly those with ballistic accumulation or nonlinear thresholds, are unable to recover their own parameters adequately, making their usage in parameter estimation contexts questionable.

Subdiffusive Dynamics Lead to Depleted Particle Densities near Cellular Borders.

It has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean-squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different characteristics of the cellular environment can introduce different types of anomalousness. A significant majority of this literature has, however, focused on characterizing the properties of trajectories that do not interact with cell borders (e.g., cell membrane or nucleus). Numerous biological processes ranging from protein activation to exocytosis, however, require particles to be near a membrane. This study investigates the consequences of a canonical type of subdiffusive motion, fractional Brownian motion, and its physical analog, generalized Langevin equation dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of subdiffusive motion leads to the formation of significant zones of depleted particle density near boundaries and that this effect is independent of the specific model details encoding those dynamics. Rather, these depletion layers are a natural and robust consequence of the anticorrelated nature of motion increments that is at the core of fractional Brownian motion (or alternatively generalized Langevin equation) dynamics. If such depletion zones are present, it would be of profound importance given the wide array of signaling and transport processes that occur near membranes. If not, that would suggest our understanding of this type of anomalous motion may be flawed. Either way, this result points to the need to further investigate the consequences of anomalous particle motions near cell borders from both theoretical and experimental perspectives.

Biophysical attributes that affect CaMKII activation deduced with a novel spatial stochastic simulation approach.

Calcium/calmodulin-dependent protein kinase II (CaMKII) holoenzymes play a critical role in decoding Ca2+ signals in neurons. Understanding how this occurs has been the focus of numerous studies including many that use models. However, CaMKII is notoriously difficult to simulate in detail because of its multi-subunit nature, which causes a combinatorial explosion in the number of species that must be modeled. To study the Ca2+-calmodulin-CaMKII reaction network with detailed kinetics while including the effect of diffusion, we have customized an existing stochastic particle-based simulator, Smoldyn, to manage the problem of combinatorial explosion. With this new method, spatial and temporal aspects of the signaling network can be studied without compromising biochemical details. We used this new method to examine how calmodulin molecules, both partially loaded and fully loaded with Ca2+, choose pathways to interact with and activate CaMKII under various Ca2+ input conditions. We found that the dependence of CaMKII phosphorylation on Ca2+ signal frequency is intrinsic to the network kinetics and the activation pattern can be modulated by the relative amount of Ca2+ to calmodulin and by the rate of Ca2+ diffusion. Depending on whether Ca2+ influx is saturating or not, calmodulin molecules could choose different routes within the network to activate CaMKII subunits, resulting in different frequency dependence patterns. In addition, the size of the holoenzyme produces a subtle effect on CaMKII activation. The more extended the subunits are organized, the easier for calmodulin molecules to access and activate the subunits. The findings suggest that particular intracellular environmental factors such as crowding and calmodulin availability can play an important role in decoding Ca2+ signals and can give rise to distinct CaMKII activation patterns in dendritic spines, Ca2+ channel nanodomains and cytoplasm.

Parallel probability density approximation.

Probability density approximation (PDA) is a nonparametric method of calculating probability densities. When integrated into Bayesian estimation, it allows researchers to fit psychological processes for which analytic probability functions are unavailable, significantly expanding the scope of theories that can be quantitatively tested. PDA is, however, computationally intensive, requiring large numbers of Monte Carlo simulations in order to attain good precision. We introduce Parallel PDA (pPDA), a highly efficient implementation of this method utilizing the Armadillo C++ and CUDA C libraries to conduct millions of model simulations simultaneously in graphics processing units (GPUs). This approach provides a practical solution for rapidly approximating probability densities with high precision. In addition to demonstrating this method, we fit a piecewise linear ballistic accumulator model (Holmes, Trueblood, & Heathcote, 2016) to empirical data. Finally, we conducted simulation studies to investigate various issues associated with PDA and provide guidelines for pPDA applications to other complex cognitive models.

A mathematical model coupling polarity signaling to cell adhesion explains diverse cell migration patterns.

Protrusion and retraction of lamellipodia are common features of eukaryotic cell motility. As a cell migrates through its extracellular matrix (ECM), lamellipod growth increases cell-ECM contact area and enhances engagement of integrin receptors, locally amplifying ECM input to internal signaling cascades. In contrast, contraction of lamellipodia results in reduced integrin engagement that dampens the level of ECM-induced signaling. These changes in cell shape are both influenced by, and feed back onto ECM signaling. Motivated by experimental observations on melanoma cells lines (1205Lu and SBcl2) migrating on fibronectin (FN) coated topographic substrates (anisotropic post-density arrays), we probe this interplay between intracellular and ECM signaling. Experimentally, cells exhibited one of three lamellipodial dynamics: persistently polarized, random, or oscillatory, with competing lamellipodia oscillating out of phase (Park et al., 2017). Pharmacological treatments, changes in FN density, and substrate topography all affected the fraction of cells exhibiting these behaviours. We use these observations as constraints to test a sequence of hypotheses for how intracellular (GTPase) and ECM signaling jointly regulate lamellipodial dynamics. The models encoding these hypotheses are predicated on mutually antagonistic Rac-Rho signaling, Rac-mediated protrusion (via activation of Arp2/3 actin nucleation) and Rho-mediated contraction (via ROCK phosphorylation of myosin light chain), which are coupled to ECM signaling that is modulated by protrusion/contraction. By testing each model against experimental observations, we identify how the signaling layers interact to generate the diverse range of cell behaviors, and how various molecular perturbations and changes in ECM signaling modulate the fraction of cells exhibiting each. We identify several factors that play distinct but critical roles in generating the observed dynamic: (1) competition between lamellipodia for shared pools of Rac and Rho, (2) activation of RhoA by ECM signaling, and (3) feedback from lamellipodial growth or contraction to cell-ECM contact area and therefore to the ECM signaling level.

Cell Sorting and Noise-Induced Cell Plasticity Coordinate to Sharpen Boundaries between Gene Expression Domains.

A fundamental question in biology is how sharp boundaries of gene expression form precisely in spite of biological variation/noise. Numerous mechanisms position gene expression domains across fields of cells (e.g. morphogens), but how these domains are refined remains unclear. In some cases, domain boundaries sharpen through differential adhesion-mediated cell sorting. However, boundaries can also sharpen through cellular plasticity, with cell fate changes driven by up- or down-regulation of gene expression. In this context, we have argued that noise in gene expression can help cells transition to the correct fate. Here we investigate the efficacy of cell sorting, gene expression plasticity, and their combination in boundary sharpening using multi-scale, stochastic models. We focus on the formation of hindbrain segments (rhombomeres) in the developing zebrafish as an example, but the mechanisms investigated apply broadly to many tissues. Our results indicate that neither sorting nor plasticity is sufficient on its own to sharpen transition regions between different rhombomeres. Rather the two have complementary strengths and weaknesses, which synergize when combined to sharpen gene expression boundaries.

Gene Expression Noise Enhances Robust Organization of the Early Mammalian Blastocyst.

A critical event in mammalian embryo development is construction of an inner cell mass surrounded by a trophoectoderm (a shell of cells that later form extraembryonic structures). We utilize multi-scale, stochastic modeling to investigate the design principles responsible for robust establishment of these structures. This investigation makes three predictions, each supported by our quantitative imaging. First, stochasticity in the expression of critical genes promotes cell plasticity and has a critical role in accurately organizing the developing mouse blastocyst. Second, asymmetry in the levels of noise variation (expression fluctuation) of Cdx2 and Oct4 provides a means to gain the benefits of noise-mediated plasticity while ameliorating the potentially detrimental effects of stochasticity. Finally, by controlling the timing and pace of cell fate specification, the embryo temporally modulates plasticity and creates a time window during which each cell can continually read its environment and adjusts its fate. These results suggest noise has a crucial role in maintaining cellular plasticity and organizing the blastocyst.

Bayesian analysis of the piecewise diffusion decision model.

Most past research on sequential sampling models of decision-making have assumed a time homogeneous process (i.e., parameters such as drift rates and boundaries are constant and do not change during the deliberation process). This has largely been due to the theoretical difficulty in testing and fitting more complex models. In recent years, the development of simulation-based modeling approaches matched with Bayesian fitting methodologies has opened the possibility of developing more complex models such as those with time-varying properties. In the present work, we discuss a piecewise variant of the well-studied diffusion decision model (termed pDDM) that allows evidence accumulation rates to change during the deliberation process. Given the complex, time-varying nature of this model, standard Bayesian parameter estimation methodologies cannot be used to fit the model. To overcome this, we apply a recently developed simulation-based, hierarchal Bayesian methodology called the probability density approximation (PDA) method. We provide an analysis of this methodology and present results of parameter recovery experiments to demonstrate the strengths and limitations of this approach. With those established, we fit pDDM to data from a perceptual experiment where information changes during the course of trials. This extensible modeling platform opens the possibility of applying sequential sampling models to a range of complex non-stationary decision tasks.

Models of utricular bouton afferents: role of afferent-hair cell connectivity in determining spike train regularity.

Vestibular bouton afferent terminals in turtle utricle can be categorized into four types depending on their location and terminal arbor structure: lateral extrastriolar (LES), striolar, juxtastriolar, and medial extrastriolar (MES). The terminal arbors of these afferents differ in surface area, total length, collecting area, number of boutons, number of bouton contacts per hair cell, and axon diameter (Huwe JA, Logan CJ, Williams B, Rowe MH, Peterson EH. J Neurophysiol 113: 2420-2433, 2015). To understand how differences in terminal morphology and the resulting hair cell inputs might affect afferent response properties, we modeled representative afferents from each region, using reconstructed bouton afferents. Collecting area and hair cell density were used to estimate hair cell-to-afferent convergence. Nonmorphological features were held constant to isolate effects of afferent structure and connectivity. The models suggest that all four bouton afferent types are electrotonically compact and that excitatory postsynaptic potentials are two to four times larger in MES afferents than in other afferents, making MES afferents more responsive to low input levels. The models also predict that MES and LES terminal structures permit higher spontaneous firing rates than those in striola and juxtastriola. We found that differences in spike train regularity are not a consequence of differences in peripheral terminal structure, per se, but that a higher proportion of multiple contacts between afferents and individual hair cells increases afferent firing irregularity. The prediction that afferents having primarily one bouton contact per hair cell will fire more regularly than afferents making multiple bouton contacts per hair cell has implications for spike train regularity in dimorphic and calyx afferents.NEW & NOTEWORTHY Bouton afferents in different regions of turtle utricle have very different morphologies and afferent-hair cell connectivities. Highly detailed computational modeling provides insights into how morphology impacts excitability and also reveals a new explanation for spike train irregularity based on relative numbers of multiple bouton contacts per hair cell. This mechanism is independent of other proposed mechanisms for spike train irregularity based on ionic conductances and can explain irregularity in dimorphic units and calyx endings.

Analysis of a minimal Rho-GTPase circuit regulating cell shape.

Networks of Rho-family GTPases regulate eukaryotic cell polarization and motility by controlling assembly and contraction of the cytoskeleton. The mutually inhibitory Rac-Rho circuit is emerging as a central, regulatory hub that can affect the shape and motility phenotype of eukaryotic cells. Recent experimental manipulation of the amounts of Rac and Rho or their regulators (guanine nucleotide-exchange factors, GTPase-activating proteins, guanine nucleotide dissociation inhibitors) have been shown to bias the prevalence of these different states and promote transitions between them. Here we show that part of this data can be understood in terms of inherent Rac-Rho mutually inhibitory dynamics. We analyze a spatio-temporal mathematical model of Rac-Rho dynamics to produce a detailed set of predictions of how parameters such as GTPase rates of activation and total amounts affect cell decisions (such as Rho-dominated contraction, Rac-dominated spreading, and spatially segregated Rac-Rho polarization). We find that in some parameter regimes, a cell can take on any of these three fates depending on its environment or stimuli. We also predict how experimental manipulations (corresponding to parameter variations) can affect cell shapes observed. Our methods are based on local perturbation analysis (a kind of nonlinear stability analysis), and an approximation of nonlinear feedback by sharp switches. We compare the Rac-Rho model to an even simpler single-GTPase ('wave-pinning') model and demonstrate that the overall behavior is inherent to GTPase properties, rather than stemming solely from network topology.

Is cell migration or proliferation dominant in the formation of linear arrays of oligodendrocytes?

Oligodendrocytes are the myelin-producing cells of the central nervous system that are responsible for electrically insulating axons to speed the propagation of electrical impulses. A striking feature of oligodendrocyte development within white matter is that the cell bodies of many oligodendrocyte progenitor cells become organised into discrete linear arrays of three or more cells before they differentiate into myelin-producing oligodendrocytes. These linear arrays align parallel to the direction of the axons within white matter tracts and are believed to play an important role in the co-ordination of myelination. Guided by experimental data on the abundance and composition of linear arrays in the corpus callosum of the postnatal mouse brain, we construct discrete and continuous models of linear array generation to specifically investigate the relative influence of cell migration, proliferation, differentiation and death of oligodendroglia upon the genesis of linear arrays during early postnatal development. We demonstrate that only models that incorporate significant cell migration can replicate all of the experimental observations on number of arrays, number of cells in arrays and total cell count of oligodendroglia within a given area of the corpus callosum. These models are also necessary to accurately reflect experimental data on the abundance of linear arrays composed of oligodendrocytes that derive from progenitors of different clonal origins.

The Interplay between Wnt Mediated Expansion and Negative Regulation of Growth Promotes Robust Intestinal Crypt Structure and Homeostasis.

The epithelium of the small intestinal crypt, which has a vital role in protecting the underlying tissue from the harsh intestinal environment, is completely renewed every 4-5 days by a small pool of stem cells at the base of each crypt. How is this renewal controlled and homeostasis maintained, particularly given the rapid nature of this process? Here, based on the recent observations from in vitro "mini gut" studies, we use a hybrid stochastic model of the crypt to investigate how exogenous niche signaling (from Wnt and BMP) combines with auto-regulation to promote homeostasis. This model builds on the sub-cellular element method to account for the three-dimensional structure of the crypt, external regulation by Wnt and BMP, internal regulation by Notch signaling, as well as regulation by internally generated diffusible signals. Results show that Paneth cell derived Wnt signals, which have been observed experimentally to sustain crypts in cultured organs, have a dramatically different influence on niche dynamics than does mesenchyme derived Wnt. While this signaling can indeed act as a redundant backup to the exogenous gradient, it introduces a positive feedback that destabilizes the niche and causes its uncontrolled expansion. We find that in this setting, BMP has a critical role in constraining this expansion, consistent with observations that its removal leads to crypt fission. Further results also point to a new hypothesis for the role of Ephrin mediated motility of Paneth cells, specifically that it is required to constrain niche expansion and maintain the crypt's spatial structure. Combined, these provide an alternative view of crypt homeostasis where the niche is in a constant state of expansion and the spatial structure of the crypt arises as a balance between this expansion and the action of various sources of negative regulation that hold it in check.

A new framework for modeling decisions about changing information: The Piecewise Linear Ballistic Accumulator model.

In the real world, decision making processes must be able to integrate non-stationary information that changes systematically while the decision is in progress. Although theories of decision making have traditionally been applied to paradigms with stationary information, non-stationary stimuli are now of increasing theoretical interest. We use a random-dot motion paradigm along with cognitive modeling to investigate how the decision process is updated when a stimulus changes. Participants viewed a cloud of moving dots, where the motion switched directions midway through some trials, and were asked to determine the direction of motion. Behavioral results revealed a strong delay effect: after presentation of the initial motion direction there is a substantial time delay before the changed motion information is integrated into the decision process. To further investigate the underlying changes in the decision process, we developed a Piecewise Linear Ballistic Accumulator model (PLBA). The PLBA is efficient to simulate, enabling it to be fit to participant choice and response-time distribution data in a hierarchal modeling framework using a non-parametric approximate Bayesian algorithm. Consistent with behavioral results, PLBA fits confirmed the presence of a long delay between presentation and integration of new stimulus information, but did not support increased response caution in reaction to the change. We also found the decision process was not veridical, as symmetric stimulus change had an asymmetric effect on the rate of evidence accumulation. Thus, the perceptual decision process was slow to react to, and underestimated, new contrary motion information.